Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The early stage behaviour of a stochastic SIR epidemic with term-time forcing
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 46, no 4, 975-992 p.Article in journal (Refereed) Published
Abstract [en]

The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An 'environment' in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here 'term-time forcing' refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {A(t)}<sub>t≥0</sub>. Threshold conditions in terms of R<sub>⋆</sub> are obtained, such that R<sub>⋆</sub> > 1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen.

Place, publisher, year, edition, pages
2009. Vol. 46, no 4, 975-992 p.
Keyword [en]
branching process in a seasonal environment, seasonal forcing, Stochastic epidemic, term-time forcing, threshold conditions
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-35205DOI: 10.1239/jap/1261670683ISI: 000273995700004OAI: oai:DiVA.org:su-35205DiVA: diva2:286656
Available from: 2010-01-15 Created: 2010-01-15 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Stochastic Epidemic Models: Different Aspects of Heterogeneity
Open this publication in new window or tab >>Stochastic Epidemic Models: Different Aspects of Heterogeneity
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is concerned with the study of stochastic epidemic models for infectious diseases in heterogeneous populations. All diseases treated are of SIR type, i.e. individuals are either Susceptible, Infectious or Recovered (and immune). The transitions between these states are according to S to I to R.

The thesis consists of five papers. Papers I and II treat approximations for the distribution of the time to extinction. In Paper I, a sub-community version of the SIR model with demography is considered. The interest is in how the distribution of the time to extinction is affected by varying the degree of interaction between the sub-communities. Paper II is concerned with a two-type version of Bartlett's model. The distribution of the time to extinction is studied when the difference in susceptibility/infectivity between the types of individuals is varied.

Papers III and IV treat random intersection graphs with tunable clustering. In Paper III a Reed-Frost epidemic is run on such a random intersection graph. The critical parameter R_0 and the probability of a large outbreak are derived and it is investigated how these quantities are affected by the clustering in the graph. In Paper IV the interest is in the component structure of such a graph, i.e. the size and the emergence of a giant component is studied.

The last paper, Paper V, treats the situation when a simple epidemic is running in a varying environment. A varying environment is in this context any external factor that affects the contact rate in the population, but is itself unaffected by the population. The model treated is a term-time forced version of the stochastic general epidemic where the contact rate is modelled by an alternating renewal process. A threshold parameter R_* and the probability of a large outbreak are derived and studied.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2008. 21 p.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-8335 (URN)978-91-7155-784-1 (ISBN)
Public defence
2008-12-19, sal 14, hus 5, Kräftriket, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2008-11-27 Created: 2008-11-20 Last updated: 2012-07-02Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Britton, Tom
By organisation
Department of Mathematics
In the same journal
Journal of Applied Probability
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 45 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf